Archimedes' Volume of a Sphere Demonstration

This example visually demonstrates Archimedes' famous theorem on the volume of a sphere: the volume of a sphere is equal to two-thirds that of a cylinder with the same radius and also equal to three-halves that of a cone with the same radius. The core mathematical concepts involved include solid geometry volume calculations, geometric relationships among cylinders, cones, and spheres, exponentiation, and properties of inscribed circles. The construction leverages GeoGebra commands such as Plane, Cylinder, Cone, IntersectPath, Sphere, Polygon, and Angle, utilizing objects like n, d, a, c, e, b, f, g, h, k, p, q, i, j, r, l, poly1, a_1, b_1, c_1, poly2, m, s, t, α, β for parameterization and geometric elements. It is suitable for high school solid geometry instruction to enhance understanding and visualization of classical geometric theorems.